Separating spatial and temporal variation in multi-species ... · By Kathy Mier Alaska Fisheries...
Transcript of Separating spatial and temporal variation in multi-species ... · By Kathy Mier Alaska Fisheries...
By Kathy Mier Alaska Fisheries Science Center
Separating spatial and temporal variation in multi-species community structure using PERMANOVA, a permutational
MANOVA
Outline
• Explain mo+va+on • Provide overview of Community Structure Analyses
• Illustrate advantages of PERMANOVA over ANOSIM and BIOENV
• Give example having spa+al and temporal effects
• Describe other applica+ons
1) Does abundance of a single species vary significantly among regions or across years?
2) Does the community structure (mul+ple species as they relate to each other in terms of abundance or biomass) vary significantly among regions or across years?
3) Do certain environmental variables help explain any differences found?
Common questions asked by fishery biologists:
ANOVA vs. MANOVA
Species 1
Species 2
Species 3
Species 4
Site 1 25 28 1 20
Site 2 15 18 0 0
Site 3 7 10 0 0
Site 4 8 0 100 7
Species 1
Site 1 25
Site 2 15
Site 3 7
Site 4 8
univariate mul+variate
Community Structure Analyses Overview
• Ecological distance (difference) between samples/variables is defined by an appropriate dissimilarity coefficient.
• Graphical Display of community paVern • classifica+on (e.g. cluster analysis) • ordina+on (e.g. NMDS)
• Test for spa+al and/or temporal differences between predefined groups, usually using nonparametric methods.
• Determine species most responsible for groupings.
• Linking community paVerns to environmental variables.
Specialized Community Structure Software
Decorana/Twinspan
Recurrent Group (Fager)
Field data
Hypothesis Testing
(ANOSIM or PERMANOVA)
Transformation
Standardisation
Classification
Dissimilarity measure
Ordination
Spatial/Temporal Effects
Species 1
Species 2
Species 3
Species 4
Site 1 25 28 1 20
Site 2 15 18 0 0
Site 3 7 10 0 0
Site 4 8 0 100 7
Species 1
Species 2
Species 3
Species 4
Year 1 25 28 1 20
Year 2 15 18 0 0
Year 3 7 10 0 0
Year 4 8 0 100 7
Data by site Data by year (means/totals)
Test for region effect Test for warm/cold effect
Field data
Hypothesis Testing
(ANOSIM or PERMANOVA)
Transformation
Standardisation
Classification
Dissimilarity measure
Ordination
• If comparing samples (sites), then use 4th root or square root transforma+on.
• If comparing species, then standardize by species totals or maximum with no transforma+on.
Should data be standardised and /or transformed?
Field data
Hypothesis Testing
(ANOSIM or PERMANOVA)
Transformation
Standardisation
Classification
Dissimilarity measure
Ordination
Bray-Curtis Dissimilarity Coefficient
( )∑
∑
=
=
+
−= n
kkjki
n
kkjki
BCD
yy
yyjid
1,,
1,,
),(
for sites i and j, for n species
Bray-Curtis Dissimilarity
Site 1 Site 2 Site 3 Site 4 Species
1 25 28 1 20 Species
2 15 18 0 0 Species
3 7 10 0 0
Raw Data Bray-‐Cur+s of sites
Site 1 2 3 4
1 0
2 0.087 0
3 0.958 0.965 0
4 0.403 0.474 0.905 0
Field data
Hypothesis Testing
(ANOSIM or PERMANOVA)
Transformation
Standardisation
Classification
Dissimilarity measure
Ordination
Descriptive Analyses
Cluster Analysis NMDS
Field data
Hypothesis Testing
(ANOSIM or PERMANOVA)
Transformation
Standardisation
Classification
Dissimilarity measure
Ordination
One way ANOVA
Group 1 Group 2 Group 3
Why not use classical MANOVA??
• MANOVA, unlike ANOVA, is NOT robust to viola6ons of parametric assump6ons. Most ecological data is overdispersed, nonnormal (right-‐skewed), with lots of zeros.
• MANOVA requires the number of variables to be less than number of samples
What do we do?
• Use analyses based on dissimilarity coefficients
• Use permuta6on techniques that do not require parametric assump+ons, since no distribu+on is being assumed
• ANOSIM (Analysis of Similarity) • PERMANOVA (Permuta+onal MANOVA)
What is ANOSIM? (Analysis of similarity)
• A nonparametric mul+variate ANOVA using ranked distance or dissimilarity between pairs of samples or variables (Bray-‐Cur+s)
• Uses R test sta6s6c:
• Uses permuta2on techniques to compute p-‐value, therefore does not assume a par+cular distribu+on
)1(21 −
−=
nnrrR WB
What is “PERMANOVA”? (Permutational MANOVA)
• An extension to ANOSIM, using distance or dissimilarity between pairs of samples or variables (Bray-‐Cur+s)
• Uses Pseudo-‐F test sta6s6c:
• Uses permuta2on techniques to compute p-‐value, therefore does not assume a par+cular distribu+on
aNSSaSSF
W
A
−−
=1
Why use PERMANOVA over ANOSIM?
• PERMANOVA , uses actual Bray-‐Cur6s coefficients where ANOSIM uses only ranks of Bray-‐Cur6s, therefore preserving more informa+on
• PERMANOVA allows for par66oning of variability, similar to ANOVA, therefore allowing for more complex designs (mul+ple factors, nested factors, interac+ons, covariates)
Huygen’s theorem
i
n
pd
m
iin
ii
∑∑ =
=
= 1
2
1
2
id ip
centroid
Site 1 2 3 4
1 0
2 0.087 0
3 0.958 0.965 0
4 0.403 0.474 0.905 0
Group 1 Group 2
Group 1
Group 2
Site 1 2 3 4
1 0
2 0.087 0
3 0.958 0.965 0
4 0.403 0.474 0.905 0
SST = SS of all / N SSW = SS of each group /n
PERMANOVA partitioning of SS
SSA = SST -‐ SSW
Classic F statistic
aNSSaSS
FWithin
Among
−
−=
1
For PERMANOVA, we call this a Pseudo-‐F We cannot use a tradi+onal F table to compute the p-‐value, but must create our own distribu+on by randomly shuffling the group labels onto sample units
Pseudo-‐F (observed)
Pseudo-‐F (afer permuta+on)
Test by permutation
1).(1).(
+ʹ′+≥ʹ′
=FofnoTotalFFofNoP
Zooplankton Example 1) Was the community structure of Zooplankton different between warm (2003-‐2005) and cold years (2006-‐2009) in the Bering Sea.
2) If so, what environmental variables contributed to the difference?
From: Eisner et al. “Climate-‐mediated changes in zooplankton community structure for the eastern Bering Sea”(in prep)
Spatial/Temporal Effects
Species 1
Species 2
Species 3
Species 4
Site 1 25 28 1 20
Site 2 15 18 0 0
Site 3 7 10 0 0
Site 4 8 0 100 7
2005…2009
2004
2003
Species 1
Species 2
Species 3
Species 4
Site 1 25 28 1 20
Site 2 15 18 0 0
Site 3 7 10 0 0
Site 4 8 0 100 7
Species 1
Species 2
Species 3
Species 4
Site 1 25 28 1 20
Site 2 15 18 0 0
Site 3 7 10 0 0
Site 4 8 0 100 7
BASIS Station Locations 2003-2009 2003 2004 2005
2006 2007 2008 2009
Cold pool (< 2°C) indicated by dashed black line.
2003 2004 2005
2006 2007 2008 2009
Bottom temperature (bottom 10m)
warm
cold
NMDS plot of all stations and years
NMDS of all stations and years
How do we account for uneven sampling across years?
And how do we tease out the spatial
variability from the temporal variability?
Crea2ng spa2al “Blocks”
Does community structure differ between warm and cold years?
S Inner
PERMANOVA table of results
Source df SS MS Pseudo-‐F P(perm)
Regime 1 8515.8 8515.8 2.8989 0.002 Significant Regime effect over and above the varia+on of this effect among blocks
Block 21 23486 1118.4 1.7107 0.001
Year(Regime) 5 12584 2516.8 3.85 0.001
RegimexBlock** 20 20055 1002.7 1.5339 0.002
Res 78 50991 653.73
Total 125 1.22E+05
** Term has one or more empty cells
What environmental variables help explain the difference between
warm and cold years?
16 environmental variables
From Niskin bottle samples:
Nitrate and ammonium (at surface and below pycnocline) Chlorophyll a from surface Percentage of large phytoplankton (>10 micrometers/total chl a)
From CTD:
Temperature and salinity averaged over mixed layer depth Temperature and salinity averaged over water below the pycnocline Chlorophyll a determined by fluorescence (fluorometer on CTD), Stability over the top 70m, Day of sea ice retreat % time in upwelling
Lattitude and Longitude
Why not use BIO-ENV?
What is BIOENV?
BIOENV (or BEST) is an itera+ve procedure in PRIMER that links environmental variables to community structure by seeking the best subset of environmental variables that explains the community structure.
PERMANOVA vs. BIOENV
We did not use BIOENV in this case because we wanted to remove the spa6al effects, so that we could tease out what was driving the temporal effects only (specifically, warm vs. cold years).
Does community structure differ between warm and cold years?
S Inner
PERMANOVA table of results
Source df SS MS Pseudo-‐F P(perm)
Regime 1 8515.8 8515.8 2.8989 0.002 Significant Regime effect over and above the varia+on of this effect among blocks
Block 21 23486 1118.4 1.7107 0.001
Year(Regime) 5 12584 2516.8 3.85 0.001
RegimexBlock** 20 20055 1002.7 1.5339 0.002
Res 78 50991 653.73
Total 125 1.22E+05
** Term has one or more empty cells
S Inner
Source df SS MS Pseudo-‐F P(perm)
Block 21 25510 1215 1.7541 0.001
IntChlaTop50m 1 4857 4857 3.706 0.012
% Time upwelling 1 10027 10027 4.2999 0.014
T above MLD 1 2569 2569 2.8856 0.030
Regime 1 4449 4449 2.0256 0.079
Year(Regime) 4 7842 1960 2.9718 0.001 RegimexGRID 20 19086 954 1.4661 0.006
Year(Regime)xBlock 68 43242 636 1.2798 0.171 Residual 8 3975 497
Total 125 121560
Best-fit PERMANOVA with Environmental Variables
Summary of Example
• NMDS plots suggested a possible difference in community structure across regions and between warm and cold years
• PERMANOVA showed that there was a significant difference in the community structure of zooplankton between warm and cold years over and above the varia+on of this effect among blocks.
• Environmental factors that help to explain this significant Regime effect afer removing spa+al variability, include IntChlatop50m, %Time in Upwelling, and T from MLD.
Data applications of PERMANOVA
• Abundance • Biomass • Diet • Lengths • Otolith measurements • Impact studies
Recent studies using PERMANOVA or ANOSIM
Busby et al. “Spa+al and temporal paVerns in summer ichthyoplankton assemblages on the eastern Bering Sea shelf 1996-‐2007” (compares mul6-‐species abundance and lengths across years) Wilson et al. “Food-‐related benefits of rearing in an outlying region: walleye pollock off Kodiak Island, Gulf of Alaska” (analyzes pollock diet and distribu6on of zooplankton) Jump et al. “Feeding Ecology and Niche Separa+on of Juvenile Northern Rock Sole and Yellowfin Sole in the Eastern Bering Sea” (compares diets where both species co-‐occur and occur alone)
Recap • Community structure analysis is a very useful approach for mul+-‐species data because we can more precisely define dissimilarity/similarity with Bray-‐Cur+s coefficient
• Pretreatment of data is essen+al, since this drives the analysis (elimina+on of very rare species, transforma+on of samples, standardisa+on of species).
• Descrip+ve methods (classifica+on, ordina+on) allow for graphic representa+ons which may help to see whats going on.
• Hypothesis tes+ng such as ANOSIM or PERMANOVA, with PERMANOVA being more versa+le, can be applied, even if data is nonnormal.
• PERMANOVA, because it can par++on the variance as in an ANOVA, is useful for examining significant enviromental effects.
Thanks to…
• PRIMER developers, including Bob Clarke, Ray Gorley, and Mar+ Anderson for their correspondence
• Lisa Eisner and EMA group for the use of their data